The paper introduces a novel conditional independence (CI) based method for linear and nonlinear, lagged and contemporaneous causal discovery from observational time series in the causally sufficient case. Existing CI-based methods such as the PC algorithm and also common methods from other frameworks suffer from low recall and partially inflated false positives for strong autocorrelation which is an ubiquitous challenge in time series. The novel method, PCMCI$^+$, extends PCMCI [Runge et al., 2019b] to include discovery of contemporaneous links. PCMCI$^+$ improves the reliability of CI tests by optimizing the choice of conditioning sets and even benefits from autocorrelation. The method is order-independent and consistent in the oracle case. A broad range of numerical experiments demonstrates that PCMCI$^+$ has higher adjacency detection power and especially more contemporaneous orientation recall compared to other methods while better controlling false positives. Optimized conditioning sets also lead to much shorter runtimes than the PC algorithm. PCMCI$^+$ can be of considerable use in many real world application scenarios where often time resolutions are too coarse to resolve time delays and strong autocorrelation is present.
Functional differentiation in the brain emerges as distinct regions specialize and is key to understanding brain function as a complex system. Previous research has modeled this process using artificial neural networks with specific constraints. Here, we propose a novel approach that induces functional differentiation in recurrent neural networks by minimizing mutual information between neural subgroups via mutual information neural estimation. We apply our method to a 2-bit working memory task and a chaotic signal separation task involving Lorenz and R\"ossler time series. Analysis of network performance, correlation patterns, and weight matrices reveals that mutual information minimization yields high task performance alongside clear functional modularity and moderate structural modularity. Importantly, our results show that functional differentiation, which is measured through correlation structures, emerges earlier than structural modularity defined by synaptic weights. This suggests that functional specialization precedes and probably drives structural reorganization within developing neural networks. Our findings provide new insights into how information-theoretic principles may govern the emergence of specialized functions and modular structures during artificial and biological brain development.
The long horizon forecasting (LHF) problem has come up in the time series literature for over the last 35 years or so. This review covers aspects of LHF in this period and how deep learning has incorporated variants of trend, seasonality, fourier and wavelet transforms, misspecification bias reduction and bandpass filters while contributing using convolutions, residual connections, sparsity reduction, strided convolutions, attention masks, SSMs, normalization methods, low-rank approximations and gating mechanisms. We highlight time series decomposition techniques, input data preprocessing and dataset windowing schemes that improve performance. Multi-layer perceptron models, recurrent neural network hybrids, self-attention models that improve and/or address the performances of the LHF problem are described, with an emphasis on the feature space construction. Ablation studies are conducted over the ETTm2 dataset in the multivariate and univariate high useful load (HUFL) forecasting contexts, evaluated over the last 4 months of the dataset. The heatmaps of MSE averages per time step over test set series in the horizon show that there is a steady increase in the error proportionate to its length except with xLSTM and Triformer models and motivate LHF as an error propagation problem. The trained models are available here: https://bit.ly/LHFModelZoo
While adversarial robustness and generalization have individually received substantial attention in the recent literature on quantum machine learning, their interplay is much less explored. In this chapter, we address this interplay for variational quantum models, which were recently proposed as function approximators in supervised learning. We discuss recent results quantifying both robustness and generalization via Lipschitz bounds, which explicitly depend on model parameters. Thus, they give rise to a regularization-based training approach for robust and generalizable quantum models, highlighting the importance of trainable data encoding strategies. The practical implications of the theoretical results are demonstrated with an application to time series analysis.
Fast and scalable alignment of time series is a fundamental challenge in many domains. The standard solution, Dynamic Time Warping (DTW), struggles with poor scalability and sensitivity to noise. We introduce TimePoint, a self-supervised method that dramatically accelerates DTW-based alignment while typically improving alignment accuracy by learning keypoints and descriptors from synthetic data. Inspired by 2D keypoint detection but carefully adapted to the unique challenges of 1D signals, TimePoint leverages efficient 1D diffeomorphisms, which effectively model nonlinear time warping, to generate realistic training data. This approach, along with fully convolutional and wavelet convolutional architectures, enables the extraction of informative keypoints and descriptors. Applying DTW to these sparse representations yield major speedups and typically higher alignment accuracy than standard DTW applied to the full signals. TimePoint demonstrates strong generalization to real-world time series when trained solely on synthetic data, and further improves with fine-tuning on real data. Extensive experiments demonstrate that TimePoint consistently achieves faster and more accurate alignments than standard DTW, making it a scalable solution for time-series analysis. Our code is available at https://github.com/BGU-CS-VIL/TimePoint
To be fully useful for public health practice, models for epidemic response must be able to do more than predict -- it is also important to incorporate the mechanisms underlying transmission dynamics to enable policymakers and practitioners to be able to evaluate what-if scenarios and intervention options. However, most mechanistic models suffer from uncertainty in both the parameters (e.g., parameter unidentifiability) and the model structure itself, which can hinder both successful parameter estimation and model interpretation. To enable rapid development of interpretable and parsimonious mechanistic models, we use penalized regression and covariate selection methods to integrate parameter identifiability and model selection directly into the parameter estimation procedure for (in this case) traditional ordinary differential equation (ODE) models. For both simulated and real-world epidemiological data, we demonstrate that the LASSO-ODE framework is highly effective in selecting a parsimonious, identifiable model from larger, more realistic but potentially unidentifiable models, from realistically sparse data with only a single measured compartment and multiple latent (unobserved) variables. While we focus on epidemic models in this paper as a case study, these same approaches are applicable to a wide range of application areas that are faced with relatively sparse data but a need for realistic mechanistic models (e.g. mathematical oncology and mathematical biology more broadly). Additionally, the cross-validation techniques designed for time series data introduced in our study can be used across a range of time series analysis and modeling approaches.
The growing use of smartphones and IoT devices necessitates efficient time-series analysis on resource-constrained hardware, which is critical for sensing applications such as human activity recognition and air quality prediction. Recent efforts in hardware-aware neural architecture search (NAS) automate architecture discovery for specific platforms; however, none focus on general time-series analysis with edge deployment. Leveraging the problem-solving and reasoning capabilities of large language models (LLM), we propose MONAQ, a novel framework that reformulates NAS into Multi-Objective Neural Architecture Querying tasks. MONAQ is equipped with multimodal query generation for processing multimodal time-series inputs and hardware constraints, alongside an LLM agent-based multi-objective search to achieve deployment-ready models via code generation. By integrating numerical data, time-series images, and textual descriptions, MONAQ improves an LLM's understanding of time-series data. Experiments on fifteen datasets demonstrate that MONAQ-discovered models outperform both handcrafted models and NAS baselines while being more efficient.
Artefacts compromise clinical decision-making in the use of medical time series. Pulsatile waveforms offer probabilities for accurate artefact detection, yet most approaches rely on supervised manners and overlook patient-level distribution shifts. To address these issues, we introduce a generalised label-free framework, GenClean, for real-time artefact cleaning and leverage an in-house dataset of 180,000 ten-second arterial blood pressure (ABP) samples for training. We first investigate patient-level generalisation, demonstrating robust performances under both intra- and inter-patient distribution shifts. We further validate its effectiveness through challenging cross-disease cohort experiments on the MIMIC-III database. Additionally, we extend our method to photoplethysmography (PPG), highlighting its applicability to diverse medical pulsatile signals. Finally, its integration into ICM+, a clinical research monitoring software, confirms the real-time feasibility of our framework, emphasising its practical utility in continuous physiological monitoring. This work provides a foundational step toward precision medicine in improving the reliability of high-resolution medical time series analysis
This study investigates the application of novel model architectures and large-scale foundational models in temporal series analysis of lower limb rehabilitation motion data, aiming to leverage advancements in machine learning and artificial intelligence to empower active rehabilitation guidance strategies for post-stroke patients in limb motor function recovery. Utilizing the SIAT-LLMD dataset of lower limb movement data proposed by the Shenzhen Institute of Advanced Technology, Chinese Academy of Sciences, we systematically elucidate the implementation and analytical outcomes of the innovative xLSTM architecture and the foundational model Lag-Llama in short-term temporal prediction tasks involving joint kinematics and dynamics parameters. The research provides novel insights for AI-enabled medical rehabilitation applications, demonstrating the potential of cutting-edge model architectures and large-scale models in rehabilitation medicine temporal prediction. These findings establish theoretical foundations for future applications of personalized rehabilitation regimens, offering significant implications for the development of customized therapeutic interventions in clinical practice.
Time series analysis (TSA) is a longstanding research topic in the data mining community and has wide real-world significance. Compared to "richer" modalities such as language and vision, which have recently experienced explosive development and are densely connected, the time-series modality remains relatively underexplored and isolated. We notice that many recent TSA works have formed a new research field, i.e., Multiple Modalities for TSA (MM4TSA). In general, these MM4TSA works follow a common motivation: how TSA can benefit from multiple modalities. This survey is the first to offer a comprehensive review and a detailed outlook for this emerging field. Specifically, we systematically discuss three benefits: (1) reusing foundation models of other modalities for efficient TSA, (2) multimodal extension for enhanced TSA, and (3) cross-modality interaction for advanced TSA. We further group the works by the introduced modality type, including text, images, audio, tables, and others, within each perspective. Finally, we identify the gaps with future opportunities, including the reused modalities selections, heterogeneous modality combinations, and unseen tasks generalizations, corresponding to the three benefits. We release an up-to-date GitHub repository that includes key papers and resources.
Multi-modal time series analysis has recently emerged as a prominent research area in data mining, driven by the increasing availability of diverse data modalities, such as text, images, and structured tabular data from real-world sources. However, effective analysis of multi-modal time series is hindered by data heterogeneity, modality gap, misalignment, and inherent noise. Recent advancements in multi-modal time series methods have exploited the multi-modal context via cross-modal interactions based on deep learning methods, significantly enhancing various downstream tasks. In this tutorial and survey, we present a systematic and up-to-date overview of multi-modal time series datasets and methods. We first state the existing challenges of multi-modal time series analysis and our motivations, with a brief introduction of preliminaries. Then, we summarize the general pipeline and categorize existing methods through a unified cross-modal interaction framework encompassing fusion, alignment, and transference at different levels (\textit{i.e.}, input, intermediate, output), where key concepts and ideas are highlighted. We also discuss the real-world applications of multi-modal analysis for both standard and spatial time series, tailored to general and specific domains. Finally, we discuss future research directions to help practitioners explore and exploit multi-modal time series. The up-to-date resources are provided in the GitHub repository: https://github.com/UConn-DSIS/Multi-modal-Time-Series-Analysis
Large language models (LLMs) have been increasingly used in time series analysis. However, the potential of multimodal LLMs (MLLMs), particularly vision-language models, for time series remains largely under-explored. One natural way for humans to detect time series anomalies is through visualization and textual description. Motivated by this, we raise a critical and practical research question: Can multimodal LLMs perform time series anomaly detection? To answer this, we propose VisualTimeAnomaly benchmark to evaluate MLLMs in time series anomaly detection (TSAD). Our approach transforms time series numerical data into the image format and feed these images into various MLLMs, including proprietary models (GPT-4o and Gemini-1.5) and open-source models (LLaVA-NeXT and Qwen2-VL), each with one larger and one smaller variant. In total, VisualTimeAnomaly contains 12.4k time series images spanning 3 scenarios and 3 anomaly granularities with 9 anomaly types across 8 MLLMs. Starting with the univariate case (point- and range-wise anomalies), we extend our evaluation to more practical scenarios, including multivariate and irregular time series scenarios, and variate-wise anomalies. Our study reveals several key insights: 1) MLLMs detect range- and variate-wise anomalies more effectively than point-wise anomalies. 2) MLLMs are highly robust to irregular time series, even with 25% of the data missing. 3) Open-source MLLMs perform comparably to proprietary models in TSAD. While open-source MLLMs excel on univariate time series, proprietary MLLMs demonstrate superior effectiveness on multivariate time series. To the best of our knowledge, this is the first work to comprehensively investigate MLLMs for TSAD, particularly for multivariate and irregular time series scenarios. We release our dataset and code at https://github.com/mllm-ts/VisualTimeAnomaly to support future research.
Recent advancements have progressively incorporated frequency-based techniques into deep learning models, leading to notable improvements in accuracy and efficiency for time series analysis tasks. However, the Mid-Frequency Spectrum Gap in the real-world time series, where the energy is concentrated at the low-frequency region while the middle-frequency band is negligible, hinders the ability of existing deep learning models to extract the crucial frequency information. Additionally, the shared Key-Frequency in multivariate time series, where different time series share indistinguishable frequency patterns, is rarely exploited by existing literature. This work introduces a novel module, Adaptive Mid-Frequency Energy Optimizer, based on convolution and residual learning, to emphasize the significance of mid-frequency bands. We also propose an Energy-based Key-Frequency Picking Block to capture shared Key-Frequency, which achieves superior inter-series modeling performance with fewer parameters. A novel Key-Frequency Enhanced Training strategy is employed to further enhance Key-Frequency modeling, where spectral information from other channels is randomly introduced into each channel. Our approach advanced multivariate time series forecasting on the challenging Traffic, ECL, and Solar benchmarks, reducing MSE by 4%, 6%, and 5% compared to the previous SOTA iTransformer. Code is available at this GitHub Repository: https://github.com/Levi-Ackman/ReFocus.
Recent advancements in transformer-based models have greatly improved time series analysis, providing robust solutions for tasks such as forecasting, anomaly detection, and classification. A crucial element of these models is positional encoding, which allows transformers to capture the intrinsic sequential nature of time series data. This survey systematically examines existing techniques for positional encoding in transformer-based time series models. We investigate a variety of methods, including fixed, learnable, relative, and hybrid approaches, and evaluate their effectiveness in different time series classification tasks. Furthermore, we outline key challenges and suggest potential research directions to enhance positional encoding strategies. By delivering a comprehensive overview and quantitative benchmarking, this survey intends to assist researchers and practitioners in selecting and designing effective positional encoding methods for transformer-based time series models.
In this paper, we propose a novel approach that enhances recurrent neural networks (RNNs) by incorporating path signatures into their gating mechanisms. Our method modifies both Long Short-Term Memory (LSTM) and Gated Recurrent Unit (GRU) architectures by replacing their forget and reset gates, respectively, with learnable path signatures. These signatures, which capture the geometric features of the entire path history, provide a richer context for controlling information flow through the network's memory. This modification allows the networks to make memory decisions based on the full historical context rather than just the current input and state. Through experimental studies, we demonstrate that our Signature-LSTM (SigLSTM) and Signature-GRU (SigGRU) models outperform their traditional counterparts across various sequential learning tasks. By leveraging path signatures in recurrent architectures, this method offers new opportunities to enhance performance in time series analysis and forecasting applications.
Time series analysis has witnessed the inspiring development from traditional autoregressive models, deep learning models, to recent Transformers and Large Language Models (LLMs). Efforts in leveraging vision models for time series analysis have also been made along the way but are less visible to the community due to the predominant research on sequence modeling in this domain. However, the discrepancy between continuous time series and the discrete token space of LLMs, and the challenges in explicitly modeling the correlations of variates in multivariate time series have shifted some research attentions to the equally successful Large Vision Models (LVMs) and Vision Language Models (VLMs). To fill the blank in the existing literature, this survey discusses the advantages of vision models over LLMs in time series analysis. It provides a comprehensive and in-depth overview of the existing methods, with dual views of detailed taxonomy that answer the key research questions including how to encode time series as images and how to model the imaged time series for various tasks. Additionally, we address the challenges in the pre- and post-processing steps involved in this framework and outline future directions to further advance time series analysis with vision models.
Large language models (LLMs) exhibit remarkable capabilities in visual inspection of medical time-series data, achieving proficiency comparable to human clinicians. However, their broad scope limits domain-specific precision, and proprietary weights hinder fine-tuning for specialized datasets. In contrast, small specialized models (SSMs) excel in targeted tasks but lack the contextual reasoning required for complex clinical decision-making. To address these challenges, we propose ConMIL (Conformalized Multiple Instance Learning), a decision-support SSM that integrates seamlessly with LLMs. By using Multiple Instance Learning (MIL) to identify clinically significant signal segments and conformal prediction for calibrated set-valued outputs, ConMIL enhances LLMs' interpretative capabilities for medical time-series analysis. Experimental results demonstrate that ConMIL significantly improves the performance of state-of-the-art LLMs, such as ChatGPT4.0 and Qwen2-VL-7B. Specifically, \ConMIL{}-supported Qwen2-VL-7B achieves 94.92% and 96.82% precision for confident samples in arrhythmia detection and sleep staging, compared to standalone LLM accuracy of 46.13% and 13.16%. These findings highlight the potential of ConMIL to bridge task-specific precision and broader contextual reasoning, enabling more reliable and interpretable AI-driven clinical decision support.
Time series analysis has become crucial in various fields, from engineering and finance to healthcare and social sciences. In this paper, we present a comprehensive review and evaluation of time series embedding methods for effective representations in machine learning and deep learning models. We introduce a taxonomy of embedding techniques, categorizing them based on their theoretical foundations and application contexts. Unlike previous surveys, our work provides a quantitative evaluation of representative methods from each category by assessing their performance on downstream classification tasks across diverse real-world datasets. Our experimental results demonstrate that the performance of embedding methods varies significantly depending on the dataset and classification algorithm used, highlighting the importance of careful model selection and extensive experimentation for specific applications, including engineering systems. To facilitate further research and practical applications, we provide an open-source code repository implementing these embedding methods. This study contributes to the field by offering a systematic comparison of time series embedding techniques, guiding practitioners in selecting appropriate methods for their specific applications, and providing a foundation for future advancements in time series analysis.
Gaussian processes (GPs) are flexible, probabilistic, non-parametric models widely employed in various fields such as spatial statistics and machine learning. A drawback of Gaussian processes is their computational cost having $\mathcal{O}(N^3)$ time and $\mathcal{O}(N^2)$ memory complexity which makes them prohibitive for large data sets. Numerous approximation techniques have been proposed to address this limitation. In this work, we systematically compare the accuracy of different Gaussian process approximations concerning likelihood evaluation, parameter estimation, and prediction taking into account the computational time required to perform these tasks. In other words, we analyze the trade-off between accuracy and runtime on multiple simulated and large-scale real-world data sets. We find that Vecchia approximations consistently emerge as the most accurate in almost all experiments.
Long-range sequence modeling is a crucial aspect of natural language processing and time series analysis. However, traditional models like Recurrent Neural Networks (RNNs) and Transformers suffer from computational and memory inefficiencies, especially when dealing with long sequences. This paper introduces Logarithmic Memory Networks (LMNs), a novel architecture that leverages a hierarchical logarithmic tree structure to efficiently store and retrieve past information. LMNs dynamically summarize historical context, significantly reducing the memory footprint and computational complexity of attention mechanisms from O(n2) to O(log(n)). The model employs a single-vector, targeted attention mechanism to access stored information, and the memory block construction worker (summarizer) layer operates in two modes: a parallel execution mode during training for efficient processing of hierarchical tree structures and a sequential execution mode during inference, which acts as a memory management system. It also implicitly encodes positional information, eliminating the need for explicit positional encodings. These features make LMNs a robust and scalable solution for processing long-range sequences in resource-constrained environments, offering practical improvements in efficiency and scalability. The code is publicly available under the MIT License on GitHub: https://github.com/AhmedBoin/LogarithmicMemory.